Here’s quite a useful video explaining the format and pacing differences between modern and classic Doctor Who, and some options for getting more enjoyment out of the classic series.
The alternating storyline method may sound a bit confusing, but this is how I watched The Aztecs, Spearhead from Space, and Pyramids of Mars right after they became available at Amazon. I watched the first episode of each, then the second episode of each, etc. This gives the cliffhangers time to steep in. You’d think it’d be confusing, but it really isn’t any more confusing than watching three separate sitcoms on any given weeknight, as the differences between the storylines are great enough to keep them separated.